Which of the following numbers is a multiple of 5? ${47,53,86,100,106}$
The multiples of $5$ are $5$ $10$ $15$ $20$ ..... In general, any number that leaves no remainder when divided by $5$ is considered a multiple of $5$ We can start by dividing each of our answer choices by $5$ $47 \div 5 = 9\text{ R }2$ $53 \div 5 = 10\text{ R }3$ $86 \div 5 = 17\text{ R }1$ $100 \div 5 = 20$ $106 \div 5 = 21\text{ R }1$ The only answer choice that leaves no remainder after the division is $100$ $ 20$ $5$ $100$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $5$ are contained within the prime factors of $100$ $100 = 2\times2\times5\times5 5 = 5$ Therefore the only multiple of $5$ out of our choices is $100$. We can say that $100$ is divisible by $5$.